An massless equilateral triangle E F G$ of side ' a ' (As shown in figure)


An massless equilateral triangle $E F G$ of side ' $a$ ' (As shown in figure) has three particles of mass $m$ situated at its vertices. The moment of inertia of the system about the

line $E X$ perpendicular to $E G$ in the plane of $E F G$ is $\frac{N}{20} m a^{2}$

where $N$ is an integer. The value of $N$ is



Moment of inertia of the system about axis $X E$.


$\Rightarrow I=m\left(r_{E}\right)^{2}+m\left(r_{F}\right)^{2}+m\left(r_{G}\right)^{2}$

$\Rightarrow I=m \times 0^{2}+m\left(\frac{a}{2}\right)^{2}+m a^{2}=\frac{5}{4} m a^{2}=\frac{25}{20} m a^{2}$

$\therefore N=25$

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